English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We obtain some sharp estimates for the $p$-torsion of convex planar domainsin terms of their area, perimeter, and inradius. The approach we adopt relieson the use of web functions (i.e. functions depending only on the distance fromthe boundary), and on the behaviour of the inner parallel sets of convexpolygons. As an application of our isoperimetric inequalities, we consider theshape optimization problem which consists in maximizing the $p$-torsion amongpolygons having a given number of vertices and a given area. A long-standingconjecture by P\'olya-Szeg\"o states that the solution is the regular polygon.We show that such conjecture is true within the subclass of polygons for whicha suitable notion of "asymmetry measure" exceeds a critical threshold.

Sharp bounds for the p-torsion of convex planar domains